The parliament's presiding officer, George Reid, said the work to repair a beam, which swung loose earlier this year, was ahead of schedule.
Next Wednesday the MSPs will hold their first debate in the chamber since the dramatic incident, Reid said.
He said that Arup has notified the parliament that phase one is complete, and that the chamber is safe for reoccupation.
Arup's letter states: 'With the completion of these works, despite the continuing absence of the strut that swung free, we are satisfied that the chamber can be brought safely back into use'.
Reid said he was extremely pleased that MSPs would soon be allowed back into RMJM and EMBT's building.
'I want to thank all those who, under considerable pressure, stayed focused on the restoration of the roof and the continuation of parliamentary business,' he said.
'Phase one of the restoration is now complete, ensuring the safety of those who will complete phase two over the summer recess.
'Apart from a few hours on the day when the strut swung loose, we have not lost a single moment of business,' he added.